1/2 cup plus 1 teaspoon sugar
unsalted butter, cut into 1/2-inch cubes and chilled
finely grated lemon zest plus 1 teaspoon juice
Arkansas Black or Granny Smith apple, peeled, cored, and thinly sliced
large egg white, beaten
In the bowl of a standing mixer fitted with the paddle, combine the flour with 1 teaspoon of the sugar and 1/2 teaspoon of salt. Add the butter and mix at low speed until it is the size of small peas, 30 seconds. With the machine on, gradually add 1/4 cup of the ice water. Add as much of the remaining ice water as needed, 1 tablespoon at a time, until the dough is just evenly moistened (it shouldn't mass on the paddle). Turn the dough out onto a work surface and knead 2 or 3 times, just until it comes together. Pat the dough into a disk, wrap in plastic and chill for 1 hour or overnight.
Preheat the oven to 400° and line a large cookie sheet with parchment paper. On a lightly floured work surface, roll out the dough to a 17-inch round, then trim it to a neat 16-inch round. Transfer the dough to the cookie sheet.
In a medium bowl, combine the remaining 1/2 cup of sugar with the lemon zest and a pinch of salt. Add the apples and lemon juice and toss well. Arrange the apples on the dough in 2 concentric circles, leaving a 3-inch border all around. Fold the edge of the dough up and over the apples, overlapping the dough on itself as needed. Brush the rim with the egg white and sprinkle with the turbinado sugar.
Bake the pie in the center of the oven until the crust is golden and firm and the apples are tender, about 55 minutes. Transfer the cookie sheet to a rack to cool. Slide the pie onto a plate, cut into wedges and serve.